Determination of the Critical Points of Antiferromagnetic Ising Model with Next Nearest Neighbour Interactions on the Triangular Lattice

Miyashita, Seiji; Kitatani, Hidetsugu; Kanada, Yasusi

doi:10.1143/jpsj.60.1523

Cited by 23 publications

(31 citation statements)

References 16 publications

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“…Indeed, when the triangular Ising model possesses the antiferromagnetic nn interaction and ferromagnetic nnn interation, the model is known to exhibit a √ 3 × √ 3 order via the KT-type transition characterized by the exponent η = 1/4 [13][14][15][16]. Since the chirality ordering of the present model with J 2 > 0 is essntially the staggered one, it would be no surprise that the chirality ordering here is of the KT-type.…”

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confidence: 70%

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Chiral Kosterlitz-Thouless Transition in the Frustrated Heisenberg Antiferromagnet on a Pyrochlore Slab

Kawamura

Arimori

2002

Phys. Rev. Lett.

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Ordering of the geometrically frustrated two-dimensional Heisenberg antiferromagnet on a pyrochlore slab is studied by Monte Carlo simulations. In contrast to the kagomé Heisenberg antiferromagnet, the model exhibits locally non-coplanar spin structures at low temperatures, bearing nontrivial chiral degrees of freedom. Under certain conditions, the model exhibits a novel KosterlitzThouless-type transition at a finite temperature associated with these chiral degrees of freedom.

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confidence: 70%

“…[13][14][15][16] The exponent η at this second transition is believed to be 1/9 [13,16,17]. In view of this, we search for this second transition into the long-range-ordered state in our present model, but with negative result.…”

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confidence: 85%

Chiral Kosterlitz-Thouless Transition in the Frustrated Heisenberg Antiferromagnet on a Pyrochlore Slab

Kawamura

Arimori

2002

Phys. Rev. Lett.

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“…A simplification has been used in the latter approach: K nnn was taken to be nonzero only for four out of the six next-nearest neighbors [8][9][10]. This leads to a substantial simplification of the transfer matrix calculations, but FIG.…”

Section: Introductionmentioning

confidence: 99%

Triangular Ising model with nearest- and next-nearest-neighbor couplings in a field

Qian

Blöte

2004

Phys. Rev. E

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The authors study the Ising model on the triangular lattice with nearest-neighbor couplings K nn , nextnearest-neighbor couplings K nnn Ͼ 0, and a magnetic field H. This work is done by means of finite-size scaling of numerical results of transfer matrix calculations, and Monte Carlo simulations. We determine the phase diagram and confirm the character of the critical manifolds. The emphasis of this work is on the antiferromagnetic case K nn Ͻ 0, but we also explore the ferromagnetic regime K nn ജ 0 for H = 0. For K nn Ͻ 0 and H =0 we locate a critical phase presumably covering the whole range −ϱϽK nn Ͻ 0. For K nn Ͻ 0, H 0 we locate a plane of phase transitions containing a line of tricritical three-state Potts transitions. In the limit H → ϱ this line leads to a tricritical model of hard hexagons with an attractive next-nearest-neighbor potential.

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“…The critical exponent η can be estimated [47] by η = lim L1,L2→∞ η(L 1 , L 2 ) with As shown in Fig. 9, η approaches zero at low temperatures because R 2 converges to a nonzero value [see Eqs.…”

Section: E Critical Exponentmentioning

confidence: 99%

Thermal algebraic-decay charge liquid driven by competing short-range Coulomb repulsion

Kaneko¹,

Nonomura²,

Kohno³

2018

Phys. Rev. B

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We explore the possibility of a Berezinskii-Kosterlitz-Thouless-like critical phase for the charge degrees of freedom in the intermediate-temperature regime between the charge-ordered and disordered phases in two-dimensional systems with competing short-range Coulomb repulsion. As the simplest example, we investigate the extended Hubbard model with on-site and nearest-neighbor Coulomb interactions on a triangular lattice at half filling in the atomic limit by using a classical Monte Carlo method, and find a critical phase, characterized by algebraic decay of the charge correlation function, belonging to the universality class of the two-dimensional XY model with a Z6 anisotropy. Based on the results, we discuss possible conditions for the critical phase in materials. arXiv:1802.08538v2 [cond-mat.str-el]

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Determination of the Critical Points of Antiferromagnetic Ising Model with Next Nearest Neighbour Interactions on the Triangular Lattice

Cited by 23 publications

References 16 publications

Chiral Kosterlitz-Thouless Transition in the Frustrated Heisenberg Antiferromagnet on a Pyrochlore Slab

Chiral Kosterlitz-Thouless Transition in the Frustrated Heisenberg Antiferromagnet on a Pyrochlore Slab

Triangular Ising model with nearest- and next-nearest-neighbor couplings in a field

Thermal algebraic-decay charge liquid driven by competing short-range Coulomb repulsion

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